This table shows individual jelly bean colour frequencies, however due to the similarity of green and yellow jelly beans, results may be subject to human error as either one could be mistaken for the other. It has a degrees of freedom of 20 which means that there are too many factors which will interfere with the accuracy of the results.
Black
Green / Yellow
Orange
Red
total
4
5
7
4
20
12
8
0
0
20
5
8
5
2
20
5
15
0
0
20
7
6
3
4
20
6
14
0
0
20
39
56
15
10
120
This is the updated table that has grouped together green and yellow jelly beans to be recorded into one phenotype; by combining green and yellow the degrees of freedom is reduced to 15, and therefore makes the results more accurate.
Results to show Variation
Grass 1
B
Y&G
O
R
Total
P Value
O
4
5
7
4
20
E
6.5
6.5
6.5
6.5
20
O-E
-2.5
5
0.5
-2.5
(O-E)^2
6.25
5
0.25
6.25
24
(O-E)^2/E
0.961538
5
0.038462
0.961538
6.961538462
0.958
Shrub 1
B
Y&G
O
R
Total
P value
O
12
8
0
0
20
E
6.5
6.5
6.5
6.5
26
O-E
5.5
1.5
-6.5
-6.5
(O-E)^2
30.25
2.25
42.25
42.25
117
(O-E)^2/E
4.653846154
0.346153846
6.5
6.5
18
0.2627
Grass 2
B
Y&G
O
R
Total
P value
O
5
8
5
2
20
E
6.5
6.5
6.5
6.5
26
O-E
-1.5
1.5
-1.5
-4.5
-6
(O-E)^2
2.25
2.25
2.25
20.25
27
(O-E)^2/E
0.346154
0.346154
0.346154
3.115385
4.153846154
0.9972
Shrub 2
B
Y&G
O
R
Total
P value
O
5
15
0
0
20
E
6.5
6.5
6.5
6.5
26
O-E
-1.5
8.5
-6.5
-6.5
-6
(O-E)^2
2.25
72.25
42.25
42.25
159
(O-E)^2/E
0.346153846
11.11538462
6.5
6.5
24.46153846
0.0577
Grass 3
B
Y&G
O
R
Total
P value
O
7
6
3
4
20
E
6.5
6.5
6.5
6.5
26
O-E
0.5
-0.5
-3.5
-2.5
-6
(O-E)^2
0.25
0.25
12.25
6.25
19
(O-E)^2/E
0.038462
0.038462
1.884615
0.961538
2.923076923
0.9997
Shrub 3
B
Y&G
O
R
Total
P Value
0
O
6
14
0
0
20
E
6.5
6.5
6.5
6.5
26
O-E
-0.5
7.5
-6.5
-6.5
-6
(O-E)^2
0.25
56.25
42.25
42.25
141
(O-E)^2/E
0.038461538
8.653846154
6.5
6.5
21.69230769
0.1161
From our immediate results you can see that the P values are >0.05. Therefore any differences between the sample phenotype frequencies are statistically insignificant. This would suggest that the Null hypothesis at this stage is proven to be correct, which means the force of drift upon the population is responsible for phenotype frequency differences within the sample. However it could be also down to sampling error.
Results showing Genetic Drift
Grass (total)
B
Y&G
O
R
Total
O
16
19
15
10
60
E
5.333333
6.333333
5
3.333333
20
O-E
-12
-14
-8
-6
-11
-11
-10
-8
-9
-13
-12
-6
(O-E)^2
144
196
64
36
121
121
100
64
81
169
144
36
(O-E)^2/E
27
30.94737
12.8
10.8
81.54736842
22.6875
19.10526
20
19.2
80.99276316
15.1875
26.68421
28.8
10.8
81.47171053
Total
64.875
76.73684
61.6
40.8
P Value
0.0001
0.0001
0.0001
0.0001
Shrub(total)
B
Y&G
O
R
Total
O
23
37
0
0
60
E
7.666666667
12.33333333
0
0
20
O-E
-11
-29
0
0
-18
-22
0
0
-17
-23
0
0
(O-E)^2
121
841
0
0
324
484
0
0
289
529
0
0
(O-E)^2/E
15.7826087
68.18918919
0
0
83.97179788
42.26086957
39.24324324
0
0
81.50411281
37.69565217
42.89189189
0
0
80.58754407
Total
95.73913043
150.3243243
0
0
P Value
0.0001
0.0001
1
1
Our P values for the majority of the two tables are significant as they are under 0.05, this would suggest that the differences are likely due to selection and not by chance. However it is still possible it could be down to sampling error. However there were no "Orange" or "Red" phenotype jelly beans found in the schrub which would give the p value of 1.
Results showing Gene-flow
B
Y&G
O
R
Average Grass
5.333333
6.333333
5
3.333333
Average Shrub
7.666667
12.33333
0
0
Expected
6.5
9.333333
2.5
1.666667
O-E
-1.16667
-3
2.5
1.666667
1.166667
3
-2.5
-1.66667
(O-E)^2
1.361112
9.000001
6.25
2.777777
1.852625
81.00002
39.0625
7.716046
(O-E)^2/E
0.209402
0.964286
2.5
1.666667
0.285019
8.678574
15.625
4.629628
Chi^2
0.494421
9.642859
18.125
6.296295
P Value
0.9201
0.0219
0.0004
0.0981
P values for the "Black" and "Red" phenotypes of the jelly beans suggests that the results are not significant, as they are higher than the 5% significance.Results such as this could be caused by sampling error or genetic drift and would show that gene-flow has no influence to those two phenotypes. However, the "Yellow & Green" and "Orange" phenotypes have a much lower value and being within the 5% significance showing that gene-flow influences the phenotypes "Yellow & Green" and "Orange".
Results to show Variation
From our immediate results you can see that the P values are >0.05. Therefore any differences between the sample phenotype frequencies are statistically insignificant. This would suggest that the Null hypothesis at this stage is proven to be correct, which means the force of drift upon the population is responsible for phenotype frequency differences within the sample. However it could be also down to sampling error.
Results showing Genetic Drift
Results showing Gene-flow